Question: Divide the polynomials.
Usually, there are many different ways to divide polynomials. Here, we will use the method of splitting the quotient into multiple quotients: $\dfrac{2x^4+5x+4}{x}=\dfrac{2x^4}{x}+\dfrac{5x}{x}+\dfrac{4}{x}$ Now let's try to cancel common factors in the resulting terms. $\begin{aligned} \dfrac{2x^4}{x}&=2x^3 \\\\ \dfrac{5x}{x}&=5 \end{aligned}$ $\dfrac{4}{x}$ doesn't have common factors so it has to stay as it is. In conclusion, this is the result of dividing the polynomials: $2x^3+5+\dfrac{4}{x}$ [I want to see a different way of performing the division.]